Related papers: Ergodicity of the geodesic flow for groups with a …

Given a geodesic metric space $X$, we construct a corresponding hyperbolic space, which we call the contraction space, that detects all strongly contracting directions in the following sense; a geodesic in $X$ is strongly contracting if and…

We describe a family of arithmetic cross-sections for geodesic flow on compact surfaces of constant negative curvature based on the study of generalized Bowen-Series boundary maps associated to cocompact torsion-free Fuchsian groups and…

Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$ and let $\Omega$ be a 2-form. We show that the magnetic flow of the pair $(g,\Omega)$ has zero asymptotic Maslov index and zero Liouville action if and only $g$ has…

In a previous paper, the authors extended Mirzakhani's (almost-everywhere defined) measurable conjugacy between the earthquake and horocycle flows to a measurable bijection. In this one, we analyze the continuity properties of this map and…

We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…

By looking at the relationship between the recurrence properties of a countable group action with a quasi-invariant measure and the structure of its ergodic components we establish a simple general description of the Hopf decomposition of…

The paper considers the nonlinear electrodynamics type model and its relation with relativistic hydrodynamics with no dissipation (including string and membrane hydrodynamics). We are able to convert arbitrary flux of fluid to the family of…

We study the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. In particular, we prove that nonproperness entails the presence of lightlike geodesic…

We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect…

We use covariant techniques to examine the implications of the dynamical equivalence between geodesic motions and adiabatic hydrodynamic flows. Assuming that the metrics of a geodesically and a non-geodesically moving fluid are conformally…

In this paper we prove that if the geodesic flow of a {compact or non-compact} complete manifold without conjugate points is of the Anosov type, then the average of the integral of the sectional curvature along the geodesic is negative and…

The {\it curvature} and the {\it reduced curvature} are basic differential invariants of the pair: (Hamiltonian system, Lagrange distribution) on the symplectic manifold. We show that negativity of the curvature implies that any bounded…

We investigate the harmonic map heat flow from a compact Riemannian manifold \( M \) into the moduli space \( \mathcal{M}_1 \) of unit-area flat tori, which carries a natural hyperbolic structure as the quotient \( \mathrm{SL}(2,\mathbb{Z})…

We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The…

Motivated by a question of Tsai-Tsui-Wang, we consider the rigidity of map from manifolds with positive Ricci curvature to manifolds with positive sectional curvature. We show that if the Ricci curvature of the domain dominates that of the…

We introduce a natural subset of the unit tangent bundle of a convex projective manifold, the biproximal unit tangent bundle; it is closed and invariant under the geodesic flow, and we prove that the geodesic flow is topologically mixing on…

Starting with a trivial periodic flow on $\mathbb{S}M$, the unit tangent bundle of a genus two surface, we perform a Dehn-type surgery on the manifold around a tubular neighborhood of a curve on $\mathbb{S}M$ that projects to a…

In this paper we show that a geodesic flow of a compact surface without conjugate points of genus greater than one is time-preserving semi-conjugate to a continuous expansive flow which is topologically mixing and has a local product…

A \emph{geodesic current} on a free group $F$ is an $F$-invariant measure on the set $\partial^2 F$ of pairs of distinct points of $\partial F$. The space of geodesic currents on $F$ is a natural companion of Culler-Vogtmann's Outer space…

Inspired by recent experiments of cells accumulating on anisotropic substrates, we study a two-dimensional, compressible, isotropic, active fluid in the presence of anisotropic friction. We find that regions of anisotropic friction that are…